What we do know is that the House bill will probably be approved by most Republicans, and by very few Democrats.

Likewise, it’s unclear whether Senator Harry Reid’s bill will pass the Senate. But in all likelihood, most Democrats will vote for the bill, while few Republicans will.

If the bills were radically different from each other — if one slashed spending by $4 trillion, while the other relied on a more modest mix of tax increases and revenue cuts — that would make sense. But they aren’t. Instead, the bills are quite similar, as both conservative and liberal Web sites point out.

Both bills cut discretionary spending by about the same amount, roughly $1.2 trillion depending on which benchmark is used. Both set up a bipartisan fiscal commission with special powers. Neither raises taxes, or significantly changes entitlement programs.

Most of the difference in their price tags, however, has to do with the fact that Mr. Reid’s bill would count $1 trillion from the winding down of the wars in Afghanistan and Iraq as deficit savings, while Mr. Boehner’s would not — a matter of accounting rather than a substantive difference.

The only real difference, instead, is that Mr. Boehner’s bill would require Congress to approve another increase in the debt limit early next year if it fails to approve the fiscal commission’s recommendations, while Mr. Reid’s would extend the deadline beyond the end of President Obama’s first term in one fell swoop. The bills differ, in other words, in whether there will be another vote on the debt ceiling before next year’s elections.

That isn’t to say that this is a trivial matter. Republicans might hope to extract additional deficit reduction from Democrats with another round of talks.

But the politics of another round of debt ceiling negotiations seem like a wash, with neither side having looked good in the current debate. The last few weeks may have tended to reduce the chance that Mr. Obama will retain the White House, while also reducing the chance that Republicans will retain the House.

Perhaps Republicans think that taking another bite of the debt-ceiling apple is a no-lose proposition — maybe you get some additional cuts and maybe you don’t. Another round of discussions in January or February, however, would carry some risks that were not present this time around. Because of the timing, the Republican presidential contenders would have to weigh in on the debate in a firmer way — and because they would be in the midst of trying to win the Iowa caucuses and the New Hampshire primaries, they might take positions that would help them with primary voters but that could harm them in November. In addition, one might expect Mr. Obama to embrace the fiscal commission’s recommendations, as he embraced those of the Gang of Six, which could give him a firmer anchor in the negotiations, something which he lacked this time around.

Maybe there are some differences in the politics of the approaches, but they don’t seem sufficient to explain why one bill would receive near-universal Republican support and the other almost none, and vice versa among Democrats.

Instead this looks to be mostly a matter of face-saving. Mr. Reid’s bill would prevent Mr. Obama from either having to exercise a veto on a short-term extension of the debt ceiling, as he has repeatedly threatened — or from having his bluff called. Mr. Boehner’s bill would spare him the indignity of having to concede to a Democrat’s approach — even though, on policy terms, Mr. Reid’s bill looks more like a win for Republicans than a loss.

So we’re basically debating who gets the last bit of egg on his face — Mr. Boehner or Mr. Obama. (At this point, each already has more than enough to make a soufflé.)

Does that imply, by the way, that the crisis is likely to be resolved one way or another?

Probably. Markets are off again today, but I think they may be misreading the news.

A number of Republicans will vote no on Mr. Boehner’s bill — perhaps enough to kill it. The critical fact, however, is that most will vote yes — like including some who had earlier claimed that they would not raise the debt limit under any circumstances. The bottom has not fallen out from under Mr. Boehner, as had seemed possible before. Meanwhile, there have been few Democratic objections to Mr. Reid’s approach.

What that means is that a very large majority of Congress would be willing to vote for either Mr. Reid’s bill or Mr. Boehner’s. The bill that will ultimately become law may look more like one version than the other. (There are a few items that might be bartered, like that Mr. Boehner’s bill would call for a vote on a balanced budget amendment.) But it seems unlikely that the substantive or political differences between the approaches are large enough to turn that majority into a minority once a final version is settled upon.

The downside case, rather, would have been if Mr. Boehner’s bill had received not one or two dozen potential Republican objections — but, say, 100 of them. Democrats might have thought of this as a major tactical defeat for Mr. Boehner. But it would also have called into question whether the House had a sufficient number of votes to pass any type of debt ceiling legislation at all. That risk now seems lessened. We still have a ways to go, but in my view the possibility of a debt default has substantially declined.

Nate Silver is the founder and editor in chief of FiveThirtyEight. @natesilver538